The Queen's expression of sympathy in her only public address of her historic Irish visit was very warm, heartfelt and thoughtful, Prime Minister David Cameron has said.
At a state dinner in her honour, the monarch spoke of the painful legacy suffered in centuries of conflict between Britain and Ireland.
Mr Cameron said her words would have resonated with people in Ireland.
"What she said about things that could have been done differently or not been done at all, I think will have spoken volumes to people in Ireland," he said.
In a powerful and moving address in Dublin Castle on Wednesday night, in front of 172 guests, the Queen spoke of the need to remember all those whose lives had been affected by centuries of strife.
She said the relationship had not always been straightforward but stopped short of delivering an apology for Britain's actions in Ireland, saying that looking back, both nations could have acted differently.
The Queen, whose cousin Lord Mountbatten was blown up by the IRA off the County Sligo coast in 1979, said: "It is a sad and regrettable reality that through history our islands have experienced more than their fair share of heartache, turbulence and loss.
"These events have touched us all, many of us personally, and are a painful legacy. We can never forget those who have died or been injured, or their families. To all those who have suffered as a consequence of our troubled past, I extend my sincere thoughts and deep sympathy."
At the same banquet Irish President Mary McAleese said a new chapter of partnership and friendship had opened between the two countries.
Irish Prime Minister Enda Kenny said the Queen's contribution was remarkable, adding people did not expect she would speak to the extent that she did: "I think it was a remarkable contribution in what is a remarkable state visit."
